Abstract
Generalized solvability of the classical boundary-value problems for analytic and quasiconformal functions in arbitrary Jordan domains with boundary data that are measurable with respect to the logarithmic capacity is established. Moreover, it is shown that the spaces of the found solutions have the infinite dimension. Finally, some applications to the boundary-value problems for A-harmonic functions are given.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 12, No. 3, pp. 363–389, July–August, 2015.
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Gutlyanskii, V., Ryazanov, V. & Yefimushkin, A. On the boundary-value problems for quasiconformal functions in the plane. J Math Sci 214, 200–219 (2016). https://doi.org/10.1007/s10958-016-2769-2
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DOI: https://doi.org/10.1007/s10958-016-2769-2